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Current contacts: Vasily Dolgushev, Ed Letzter, Martin Lorenz or Chelsea Walton
The Seminar usually takes place on Mondays at 1:30 PM in Room 617 on the sixth floor of Wachman Hall. Click on title for abstract.
Martin Lorenz, Temple University.
Martin Lorenz, Temple University.
Martin Lorenz, Temple University.
Adam Jacoby, Temple University.
Maria Sabitova, CUNY.
Chelsea Walton, Temple University.
-Note different day and time- Sonia Natale, University of Cordoba.
Xingting Wang, Temple University
Xingting Wang, Temple University.
Marton Hablicsek, University of Pennsylvania.
Vasily Dolgushev, Temple University
This is the first lecture in the mini-course on dessins d'enfant (child's drawings) and the Grothendieck-Teichmueller group GT. In this lecture, I will introduce the "main characters" of the story and say a few words about the motivation. In the remaining lectures of this mini-course we will talk about the material of the first two chapters of the book "Graphs on surfaces and their applications" by Lando, Zagier and Zvonkin.
Vasily Dolgushev, Temple University
A constellation is a sequence of permutations in S_n satisfying some conditions. We will talk about the cartographic group of a constellation, isomorphic (and conjugate) constellations. Finally, we will show that the braid group B_k acts on constellations of length k.
Vasily Dolgushev, Temple University
I will review the notion of the fundamental group and the notion of the covering space. I will briefly outline the classification of connected covering spaces over a connected base. The notion of the monodromy group and the notion of a normal covering will be discussed. Some examples will be given. This talk is a part of the mini-course "Graphs on Surfaces".
Vasily Dolgushev, Temple University
I plan to finish the brief review of covering spaces. This talk is a part of the mini-course "Graphs on Surfaces".
Vasily Dolgushev, Temple University
I will talk about the correspondence between constellations of length k and connected coverings of the sphere with k punctures. I will recall the Riemann-Hurwitz formula and use it to compute the genus of the covering surface corresponding to the constellation. This talk is a part of the mini-course "Graphs on Surfaces".
Rekha Biswal, The Institute of Mathematical Sciences, Chennai, India
In this talk, we will explore some (surprising) connections between representation theory, combinatorics and number theory. We are interested in studying a family of finite dimensional representations of the hyperspecial parabolic subalgebra of the twisted affine Lie algebra of type $A_2^{(2)}$. These families of modules are of a lot of interest because of their connections to the representation theory of quantum affine algebras. In a joint work with Vyjayanthi Chari and Deniz Kus, it is proved that these modules admit a decreasing filtration whose successive quotients are isomorphic to stable Demazure modules in an integrable highest weight module of sufficiently large level. In particular, we show that any stable level l-Demazure module admits a filtration by level m Demazure modules for $m > l-1$. In this talk, we shall discuss the generating functions which encode the multiplicity of a given Demazure module and prove that the generating functions of graded multiplicities define hypergeometric series and that they are related to $q$-Fibonacci polynomials defined by Carlitz in the case when $l = 1, 2$ and $m = 2, 3$. We will also see that the generating functions of numerical multiplicities are related to Chebyshev polynomials of second kind and the generating functions of graded multiplicities of Demazure modules in local Weyl modules relates to Ramanujanâ€™s fifth order mock theta functions in certain special cases.
Xingting Wang, Temple University
Poisson geometry is originated in classical mechanics where one describes the time evolution of a mechanical system by solving Hamilton's equations in terms of the Hamiltonian vector field. Recently, the development of Poisson geometry has deeply entangled with noncommutative algebra and noncommutative geometry.
In this talk, I will introduce Poisson (co)homology using Poisson enveloping algebras. I will explain the unimodularity of Poisson algebras has a close relationship with the Calabi-Yau property of their enveloping algebras. This echoes Dolgushevâ€™s result such that the deformation quantization of a Poisson algebra is a Calabi-Yau algebra if and only if the corresponding Poisson structure is unimodular.
Xingting Wang, Temple University
This is the continuation of the last week's talk.
Vasily Dolgushev, Temple University
A hypermap is a bipartite graph $G$ "drawn" on an oriented Riemann surface $S$ so that the complement $S \setminus G$ is a disjoint union of (contractible) cells. I will talk about the correspondence between hypermap and constellations of length 3. This talk is a part of the mini-course "Graphs on Surfaces".
Vasily Dolgushev, Temple University
This is the second talk about hypermaps, constellations and triangulations of surfaces. This talk is a part of the mini-course "Graphs on Surfaces".
Cris Negron, M.I.T.
I will discuss the derived Picard group of an Azumaya algebra A over an affine scheme X. The derived Picard group is a derived invariant which can be seen as a refined version of the group of auto-equivalences on the derived category of quasi-coherent sheaves over A. I will explain how this group decomposes in terms of the Picard group of X, global sections of the constant sheaf of integers on X, the stabilizer of the Brauer class of A in Aut(X), and a mysterious 2-cocycle taking values in the Picard group. We will follow the basic example of the Weyl algebra in finite characteristic throughout.
Vasily Dolgushev, Temple University
A Belyi pair is a pair $(X,f)$ where $X$ is a Riemann surface and $f$ is a holomorphic map from $X$ to the complex projective plane with the critical values $0$, $1$, and $\infty$. I will talk about the correspondence between Belyi pairs and hypermaps. I will also describe several examples. This talk is a part of the mini-course "Graphs on Surfaces".
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